Yes and no. You're right as far as you analyzed the situation.
What you left out was that while you're hauling donkey to cover you're going to be a very hard target to hit. If you stand there and draw, you're basically a stationary target and much easier to hit.
So even though you may be able to draw and return fire faster than you can make it to cover, your chances of getting shot are worse, IMO, if you stand and return fire rather than start hustling for cover.
The best of both worlds is to move fast to cover while returning fire. Unfortunately, most people can't hit squat with a handgun if they're not standing still and maintaining a good stance. Practice, practice.